Sorry if this was asked an answered eons ago, but the FAQ link is currently broken...

Why is a cubic arrangement of coils considered a good idea?

Geometrically, the dual shape, a regular tetrahedral 'diamond' seems much better, for the following reasons ( I am assuming current circulates in one direction in the circular coils, around the larger diameter):

1) with a cubic arrangement, the flow in the top and bottom coils alternately opposes and coincides with the flow in the side coils, assuming the side coils are set up to always co-incide in flow direction where they meet. In other words, with a cubic arrangement, there are always points where the adjacent flow is opposed. This must cause weak points in the induced magnetic field.

2) with a cubic arrangement, there are 6 face cusps, and eight corner cusps. With a tetrahedral arrangement, there are 8 face cusps and 6 corner cusps. The corner cusps in a cubic arrangement are formed from the flows from three coils. Either the flows in the coils do not coincide where they meet, or the 'flow' around the sides of the corner cusp consists of both clockwise and anticlockwise components, necessarily asymmetrically because there must be two in one direction and one in another.

With a tetrahedral arrangement, all faces can be made identical modulo coil orientation (mag field lines in or out at centre), ditto all corner cusps, which become symmetrical. The arrangement also seems to be able to be 'wound', that is one can trace a single wire in at one point and out at the same point which will create the current flow round all the faces.

The attached diagram shows what I mean. The arrows show current flow and the numbers show how it can be wound. You probably need to wind twice from different points to create a sturdy structure at the corner cusps.

We did look at this a long while ago as I recall.I think the interesting point was in how the fields interact at the points from the radial field rotation perspective along the conductors.Have to either find the old analysis or put pencil to paper when I get a few minutes.The face cusp dynamics also change due to field density differences as compared to a circle.

The development of atomic power, though it could confer unimaginable blessings on mankind, is something that is dreaded by the owners of coal mines and oil wells. (Hazlitt)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)

This may help. I think your illustration is consistent with early work represented by MPG-1 and MPG-2. This paper :"Some Physics Considerations of Magnetic Inertial Electrostatic Confinement: A New Concept for Spherical Converging Flow Fusion"

The truncated cube Polywell was used simply because it was the simplest polyhedron to build and test. Higher order polyhedrens were/ are (?) expected to perform better. Bussard estimated a 3-5 fold improvement compared to the truncated cube.

OK, thanks. I hadn't appreciated how the cubic arrangement looks if the 'side' faces all circulate the same way relative to the cube centre, opposite to the top and bottom. At the cost of 4 apparent dead spots where the sides approach, the arrangement approximates the truncated cube shown in the paper.

Still, what you say about a 3-5 fold improvement is quite interesting. One of the things which surprised me and moved me to think about this was a presentation, probably by Park, showing a next gen test system costing several million dollars also in the cubic arrangement. Makes you wonder at what time in the development process it would be right to take advantage of better geometries.

It is a little premature. There has been an initiative to look at and test alternate geometries, but this is on hold.More pressing is validating electron injection efficiency in an operating unit.There are trade offs in more complex polyhedrons, the main one being the physical structure requirements inside the vacuum chamber.Eventually, someone is going to test a more complex construct, but not before the cube is run.

The development of atomic power, though it could confer unimaginable blessings on mankind, is something that is dreaded by the owners of coal mines and oil wells. (Hazlitt)

What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)

A circular planform cubic magnet arangement is the simplest way to approximate the rectified cube which is one of a number of true Polywell geometries. It was a circular planform for convenience. Dr Bussard stated that he wanted to test out a WB6 size unit with square planform faces. That would leave the virtual magnets as a much closer approximation of the triangular faces of the rectified cube.

RERT wrote:OK, thanks. I hadn't appreciated how the cubic arrangement looks if the 'side' faces all circulate the same way relative to the cube centre, opposite to the top and bottom. At the cost of 4 apparent dead spots where the sides approach, the arrangement approximates the truncated cube shown in the paper.

The WB six had all the fields pointed the same direction (radially in or out). It was the gaps between the toruses that formed the virtul opposite poled magnets.

I may be confused, but 12 dead spots? I'm guessing you are counting cusps, and there are sort of 14 in the truncated cube. The corner cusps are not true point cusps, but close enough for most considerations. The purpose of the Polywell is to minimize the size- loss areas of these cusps/ dead spots. The basic mirror machine only has three cusps, two end point cusps and a circumferential equatorial cusp that goes all around the machine and , though leaks considerably. By interposing additional magnets in a way that preserves the convex conformity of the B fields, the equatorial line cusp is split into two , um... tropical linear cusps/ These are compressed between the closely approximated magnets so that most of the consequent loss area is located at the quarters. This approximates the properties of a point cusp in the corner.

Bussard, etel modeled their system such that the magnet cans were considered as mathematical lines. This trivialized the effects of ExB diffusion which was not appreciated till WB6 design. It also lead to the inclusion of the "Funny Cusp" designation. As such the lines were infinity close together (no seperation), so the corner cusps were infinatly close to being true point cusps. This closely matches the wire frame design like MPG1,2. Ignoring the falacy of the "Funny Cusps" the problem is that the corner cusps/ dead spots was over metal, so that the leakage here results in charged particles directly hitting metal. No chance for recirculation or cusp plugging (which was tried in WB5 and failed).

The appreciation for the real dimensions of the magnet cans (not the simplified mathematical line representation) led to the need for separation, and eventually also the need to minimize any bridging exposure in the previously "Funny Cusp" areas. The nubs were changed to wall standoffs. This is why a higher order polyhedren is more challenging. Each face needs to be supported from the wall separately with it's own electrical and cooling connections. Some sub assembly approach may eventually be used by grouping several magnets to a common support assembly with these sub assembies then mounted to the vacuum vessel wall. With the included injectors, etc, the space outside the magnets could become extremely crowded. Recircularion and direct conversion considerations become more complex. A higher order polyhedron may be more efficient theoretically, but practical application considerations may limit things.

The "Funny Cusp" ideology would favor square magnets with small corner loss areas, but with WB6 appreciations, ExB losses where the opposed magnets are closely approximated may negate any advantages of decreasing the corner cusp areas. You are trading ExB losses for corner area cusp losses. Some intermediate curvature may be the best compromise.

PS: The idea for the Polywell is not to eliminate cusp losses, but to minimize them without decreasing the plasma volume. In order to maintain convex B field surfaces relative to the plasma everywhere (inside the magrid) you have to have cusps. This was the problem with older manipulations of the baseline mirror machine. Cusps could be reduced or eliminated (like the cylindrical geometry where there was no equatorial line cusp) but at the expense of having local concave B fields. These promoted edge instabilities which are devastating, especially at high densities where the Polywell is expected to operate. This consideration is paramount in the Polywell concept, though it does not get the press that cusp losses do.

There is a design for a cylindrical solenoid magnet with two additional ring magnets on the ends to limit end point cusps losses more. This introduces two line cusps but they are marrow like in the Polywell. The three major differences between this and the Polywell, is quasi spherical symmetry, instead it is as short or long cylindrical symmetry and arguments can be pursued about the relative advantages. A electrostatic potential well was absent (no imbalance in plasma net neutrality). The major difference though is the straight solenoid section. The B fields are not convex, at best they are linear . With local plasma turbulence this field could be pushed out and edge instabilities results. I don't know what degree of B field convexity is needed to prevent these local excursions, but some obviously is needed. Why not curve the "solenoid "section? This three ring magnet approach has been discussed some here in other threads. At one time I thought this was the Lockheed design, but it is more convoluted and without an electrostatic potential well.

RERT wrote:Yes, you're right, my mistake: if the top & bottom coils are set to match the direction of flow where they meet the sides, the corners don't have a complete 'virtual' flow.

But that kind of gets me back to where I started: we are now up to 12 dead spots, because every coil's flow is going in the opposite direction to the flow in the coils it approaches.

R.

By "dead spots", are you refering to the "funny cusps"? Do not go by the latest wiki article on these, they have the funny cusps wrong. The funny cusps would be where the "line cusps" are shown if the magnets were square planform rather than circular.